Pattern identification systems operating by the multiple similarity method

ABSTRACT

Pattern identification systems wherein N number of different &#39;&#39;&#39;&#39;standard patterns&#39;&#39;&#39;&#39; are prepared for each &#39;&#39;&#39;&#39;reference pattern, &#39;&#39;&#39;&#39; and whether a given input pattern belongs to the category of the reference pattern or not is determined according to whether a value of the sum of the squares of N number of different similarities of the input pattern to the standard patterns, or a value of the square root thereof, exceeds or falls short of a predetermined maximum.

Unite States IlJlma et a1.

atent [541 PATTERN IDENTIFICATION SYSTEMS OPERATING BY THE MULTIPLESIMILARITY METHOD [72] Inventors: Taizo Iiiima, Tokyo-t0; Kenichi Mori,Kawasaki, both of Japan [73] Assignees: Kogyo Giiutsuin, a.k.a. Agencyof Industrial Science and Technology, Ministry of International Tradeand Industry, Japanese Government,, Tokyo-to; Tokyo Shibaura DenkiKabushiki Kaisha, a.k.a. Tokyo Shibaura Electric Co., Ltd.,Kawasaki-shi, Japan; part interest to each [22] Filed: Nov. 2, 1970 [21]Appl. No.: 85,916

[30] Foreign Application Priority Data Nov. 5, 1969 Japan ..44/88109[52] US. Cl ..340/146.3Q, 340/1463 G, 340/ 146.3 MA

[51] Int. Cl. ..G06k 9/08 [58] Field of Search ..235/197; 340/146.3,172.5; 179/1 SA Multiplying/ v Sumrning ii Circuits X on Q (A1 Aug. 29,1972 3,292,148 12/ 1966 Giuliano et a1. ..340/ 146.3

Pn'mary ExaminerMaynard R. \ivllbur Assistant Examiner-Leo. H. BoudreauAtt0rneyRobert E. Burns and Emmanuel J. Lobato ABSIRACT Patternidentification systems wherein N number of different standard patternsare prepared. for each reference pattern, and whether a given inputpattern belongs to the category of the reference pattern or not isdetermined according to whether a value of the sum of the squares of Nnumber of different similarities of the input pattern to the standardpatterns, or a value of the square root thereof, exceeds or falls shortof a predetermined maximum.

6Claims,9Drawingl\'gures quuring Circuit Sum/Square Root-CircuitSquaring Circuits Muitiplying/ Summing Circuit (Bir Sum/Square lRooiCircuits e Maximum Determining- Circuit minnows sum 1 or 4 3 6 88 267 PATENTEDwszs m2 3' 688.267

SHEET t [1F 4 Muliiplying/ F I 8 Summing il Circuits Sum/Square RootCircuit M .i=N quurlngClrculis 0 1 O zi b2| 22 l 2 Muliiplyingh/ (C) i 0Summing A) (B) (G) 2 Circuits i c I 2N 2N Y2N i Sum/Square squormqclrcwis RooiCircuiis 'e Q Maximum Determining 1 Circuit Muiriplying/Summing Circuit Squcrmg PATTERN IDENTIFICATION SYSTEMS OPERATING BY THEMULTIPLE SIMILARITY METHOD BACKGROUND OF THE INVENTION This inventionrelates to pattern identification systems. The prior art patternidentification systems have been founded mostly upon the pattem matchingscheme, wherein the identity of a given By way of explanation of thefundamental concepts of the invention, in more specific aspects thereof,coninput pattern is established according to the degree of where (f,f,,) is the linner scalar product of f(:z:) and f (:c) and is defined by(1' f0) =f f (mom (2) and [lfll is the norm of f(a;) and a positivevalue defined Now, generally, the values of the similarity S f, f.,]will be in the range of foii Especially, when f (x) is identical with f(:r),

lim f( fo( [f; fo1

Consider now a certain small number 6 which is greater than zero. It maybe regarded, according to the aforesaid pattern matching scheme, thatf(x) belongs to the category of f,,(x) if the relation lftfol (6) issatisfied and that f(x) does not belong to the category of f (x) if not.

Since the similarity S [ff is kept at constant value if f(x) is replacedby Af(x) (where A is an arbitrary constant), the pattern matching schemebased upon the degree of similarity as above may be considered aconvenient form of pattern identification in so far as those patternsare concerned which will remain essentially unaffected by such a change.Practically, however, patterns are usually subject to other variouslight deformations due to varieties of causes, so that a value of scannot possibly be made sufiiciently small if it is to be selected so asto satisfy the formula 6 for all patterns to be regarded as belonging toone and the same category. The above fact may also lead to the inverseresult that the formula 6 is satisfied even for those patterns whichhave to be excluded from the category.

The present invention has been made with a view to eliminating theforegoing difficulties attendant to the prior art.

SUMMARY OF THE lNVENTlON A principal object of the invention is toprovide pattern identification systems having improved discriminationfor patterns in different category.

The other objects of the present invention, as well as thecharacteristic features thereof, will become apparent as the inventionis further clarified by the description given hereinbelow.

sider K number of different categories. A pattern f(K) X) having N-lnumber of different slight deformations with regard to kth referencepattern f,""(x) can generally be expressed by the equation where eachg,,""(x) is the component of a linearly independent deformed pattern anda is a parameter representing the magnitude'of the deformationcomponent. It should be noted here that the formula 7 holds true wheneach a,,(k) is sufficiently small.

Suppose that, with regard to N number of different patternsf (")(x), g(")(x), g- (x), Nnumber of different standard functions as defined asN-l (k) E (k) 52:5,; k=1,2,...K (s

and that{6 is determined so as to satisfy the relation The above Formula(7) can now be rewritten as N f(k)( g uo (k)( and a value of eachexpansion coefficient C,,," is obtainable according to the equationAlthough C assumes various values, as a function with respect toparameters 01 a ----athe relation *[f, fo l is satisfied with respect toany pattern f(x) defined by the formula 7.

Therefore, if the multiple similarity S *[f, f,,""] of any given patternf(x) to the reference pattern f,,""(x) is defined by then the values ofS* Lff will be in the rangeof 0 *[flfa""] l (14) Specifically, if thepattern f(x) belongs to the kth category as defined by the formula 7, 5*f,f,,"f] 1. Hence, with regard to a certain small positive member s,whether the pattern f(x) belongs to the category of the referencepattern f,,"" (x) or not will be decided according to whether therelation *lf f""] s) is satisfied or not. This type of patternidentification provides a type of the aforementioned pattern matchingscheme.

If N l in the above pattern identification method based upon multiplesimilarity, this method conforms to the ordinary similarity-basedidentification method. It will accordingly be seen that the formermethod is a substantial outgrowth of the latter method. Since a generalpattern f(x) not belonging to the category of the reference patternf,,(x) usually includes compone nts other than "(x), ""(x), -""(x), inthat case the formula 12 does not hold true. Instead,

Then the relation of the formula is not satisfied, either, so that it isconcluded that the pattern flx) does not belong to the category of thereference pattern f t Ic1 Practically, in identification of a patternsuch as a letter and numerical figure, for example, the aforesaid regionR of x will be a twodimensional plane, with x representing atwo-dimensional position vector therein and f(x) representing a functionto define the intensity (e.g. density) of the pattern at the position x.In identification of a vocal pattern, on the other hand, 1: willrepresent a vector in a coordinate plane with the two axes thereofrespectively representing time and frequency, and F (x) will represent afunction to define loudness at a specific time and in a specificfrequency band.

Having thus outlined the fundamental concepts of the present invention,description will now be given on some preferred examples of the patternidentification system of the invention with reference to the attacheddrawings.

BRIEF DESCRIPTION OF THE DRAWINGS In the drawings:

FIG. 1(a) is a schematic diagram showing the configuration of anembodiment of the present invention, wherein the computations forobtaining the scalar products of vectorial quantities required in thepattern identification systems of the invention are carried out byoptical filter means;

FIG. 1(b) is a schematic circuit diagram of another embodiment of theinvention, wherein the above computations are carried out by electricalcircuit means by being equivalently converted into those of summationand multiplication;

FIG. 2 is a block diagram of a pattern identification system inaccordance with the present invention;

FIG. 3 is a diagram showing the configuration of an example of squaringcircuits in FIG. 2;

FIG. 4 is a diagram showing the configuration of an example of circuitsfor computing square roots of weighted sum of inputs in FIG. 2, in whichis utilized the squaring circuit of FIG. 2;

FIG. 5 is a diagram showing the configuration of an example of constantmultiplying circuit in FIG. 2;

FIG. 6 is a diagram showing the configuration of an example ofcomparison circuits in FIG. 2;

FIG. 7 is a diagram showing the configuration of an example of anediting circuit in FIG. 2; and

FIG. 8 is a block diagram of another pattern identification system inaccordance with the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS In the arrangement describedherein, the desired computations for obtaining the scalar products ofvectorial quantities may be carried out by the use of optical filtermeans, as illustrated schematically in FIG. 1(a) by way of example. Inthis case, integral calculations will be necessary according to theformula 2, given earlier in this specification, with an input patternrepresented by f and reference pattern by f,,. For executing the abovecomputations by means of an electrical circuit, since the informationcontained in a diagrammatic pattern on the two-dimensional region R canbe represented by a group of values of f(x) at a finite number of samplepoints {ml chosen in accordance with the well known sampling theorem,the formula 2 can be rewritten into the following formula according towhich only multiplication and summation are required to obtain identicalresults:

(ffD rf( r)fo r) K I (m The computations according to this formula 17can now be carried out by means of an electrical circuit illustrateddiagrammatically in FIG. 1(b) as an example. In the configuration ofthis drawing, the ratio R /R, between two electrical resistances R andR, therein is set at a value of a point of a preselected standardpattern f,,""(x,) while the amplification factor of an amplifier is madesufficiently large. If, under these conditions, voltage in proportion toinput pattern value f(x,) is supplied to the circuit from an input 1,,the following relation is obtained at an output terminal Q in accordancewith the principle of the well known analog summing amplifier circuit:

(m) =2 f( r)fo (1 N 2 (f,m lllf ml (19) is obtained. Since, N number ofdifferent functions (M 4M 1 satisfying the formulas 8 and 9 can becomputed beforehand for respective reference patterns, these can beregarded as fixed coefficients in concrete pattern identificationsystems.

FIG. 2 illustrates the configuration of a typical example of the patternidentification system described herein. In this drawing, the circuits(hereinafter referred to as the multiplying/summing circuits) forconducting the above equivalently converted multiply ing and summingcomputations to obtain the aforementioned scalar products (asillustrated in FIG. 1(b) by way of example) are marked A, while thecircuits (hereinafter referred to as the squaring circuits) forconducting squaring computations are marked B. A concrete example ofthese circuits B is illustrated in detail in FIG. 3. Further thereference character C indicates circuits (hereinafter referred to as thesum/square root circuits) capable of conducting computations forobtaining sums and their square roots (an example of these circuits C isillustrated in detail in FIG. 4), D indicates a constant multiplyingcircuit, E indicates comparison circuits and F indicates an editingcircuit (examples of these circuits D, E and F are illustrated in detailin FIGS. 5, 6 and 7, respectively).

Appropriately sampled, each input pattern may be fed into the patternidentification system of FIG. 2 from its inputs i,,---- i i,, i J as agroup [f(x,) of values of an input pattern as mentioned already. Theseinputs i i J are respectively connected to J number of input terminalsof the multiplying/summing circuits A. x x indicate a group of circuitsfor conducting the multiplying and summing computations with respect tothe functions of the input pattern supplied and N number of functions datof a first reference pattern. Output signals carrying the results ofthese computations appear at output terminals a a of this group ofcircuits. Similar computations are effected with respect to N number offunctions of each of the remaining reference patterns.

The outputs a a a a kt, a of the multiplying/summing circuits arerespectively connected to the inputs of the squaring circuits y yYet-yaw ykh ykN While the Outputs ut uv 2! bb b of these squaringcircuits are combined into groups corresponding to the respectivereference patterns, each of the groups being connected to each of thesum/square root circuits Z Z z More specifically, for the firstreference pattern, the outputs b b, are connected to the sum/square rootcircuit 2,, and so forth. Hence an electrical signal corresponding tothe left side of the formula 18 will be obtained at each of the outputse e e of the sum/square root circuits.

Also the input signals supplied from the inputs i i J are directed tothe inputs of another set of squaring circuits W W thereby to compute{f(a:,) P. The outputs c c, of these squaring circuits are connected toa sum/square root circuit z so that a signal corresponding to a value of/Tf-fi is obtained at the output e of this circuit z As defined by theformula 3, this output signal is equivalent to the norm H f H of theinput pattern supplied.

The output e of the circuit 2 is connected to the input of a constantmultiplying circuit p, so that the output d of this circuit p supplies asignal corresponding to the product of the norm f l] multiplied by aconstant coefiicient corresponding to a value of (le) on the right sideof the formula 18. Hence this output signal will carry informationcorresponding to a value of the right side of the formula 18.

Now this output signal is compared with the respective signals obtainedat the outputs e e e which carry intelligence corresponding to the leftside of the formula 18, by means of the respective comparison circuitsv,, v v thereby to detect a signal or signals which satisfy theinequality of the formula 18. Each of the comparison circuits v vincludes a maximum value detecting circuit for supplying a digitaloutput l when the signals supplied thereto satisfy the formula 18,thereby to manifest whether the input pattern f supplied belongs to thecategory of the specific reference pattern or not. The outputs g g 3,,of the comparison circuits are connected to the editing circuit S. Inevent two or more of the outputs of the comparison circuits supplyoutput l so that the identification system is incapable of making adefinite response, or in event none of the outputs supplies output 1 sothat the input pattern is unidentifiable, an output r of the editingcircuit S supplies an identification rejected output. In other cases,where the input pattern has been identified as belonging to the categoryof only one of the reference patterns, the identity of that inputpattern is exhibited at one of the outputs 0,, O 0,, which correspondsto that one reference pattern.

FIG. 3 illustrates an example of the squaring circuits given in FIG. 2.According to this particular circuit configuration, a plurality ofdiodes are interconnected in series, with a plurality of resistances Rinterposed altematingly to form a ladder network. The resistances R arecommonly interconnected at one end thereof, and a compensationresistance 2R (two times more resistive than the other resistances R) isconnected between the two inputs of the circuit. The following relationsexist in this circuit:

I= nE /2R (n l )E /R E /R n E /2R (b) E=nE n= 1,2,

where E is the input voltage, I is the current flowing through thecircuit, and E is the forward voltage drop of one diode. Eliminating nfrom the above equations,

It will now be seen that the current I flowing through the circuit ofFIG. 3 is proportionate to the square of the input voltage E.(Considered graphically, this means approximation to the characteristiccurve of the squares with broken lines. Actually, however, the diodes donot show ideal broken line characteristics but exponential functioncharacteristics, so that the squaring circuit will have a still betterdegree of approximation.)

FIG. 4 illustrates an example of the sum/square root circuits describedabove in connection with FIG. 2. According to this particular example,in which is utilized the above mentioned squaring circuit as seen in thedrawing, inputs I I J are commonly connected to the well knownoperational amplifier (amplification factor A) 0A through theirrespective resistances R in order to obtain the sum and then the squareroot of input signals. If the input voltage of the operational amplifieris E and its output voltage 0, the operational amplifier is controlledin such a manner that a current value at the input of the amplifierbecomes zero (this technique belongs to the prior art). Now, if theinput voltage of the squaring circuit SC is 6, the output currentthereof is 3'6 (B being a constant), as is obvious from the foregoingexplanation made with reference to FIG. 3, so that ER I If E iseliminated from the above equations,

HR (1, I, I =B-6 (N07 RA) (2) The second term of the right side of thepreceding equation can be reduced to a negligible value if theamplification factor A of the operational amplifier is made sufficientlylarge. Hence, if B I /R Further there is existent between the inputvoltage I and the output voltage 6 of this circuit the relation=(R,/R,)-I (g) The aforesaid constant is now obtainable if (R,/R,) l

FIG. 6 illustrates an example of the comparison circuits given in FIG.2. Broadly, this particular example is comprised of a differentialamplifier portion and a socalled Schmidt circuit portion, and adifference between the signals supplied into the comparison circuit fromits inputs I, and I is detected and amplified. If that difference isfound positive, the Schmidt circuit will supply output l saturated inpositive potential; if it is negative, the circuit will supply output 0of zero potential. Therefore, if the input I, is connected with one ofthe aforementioned outputs e,, e,,, e of the sum/square root circuits2,, 2g, 2,, given in FIG. 2, thereby to supply a signal corresponding tothe left side of the formula 18, and if the other input I is connectedwith the output d of the constant multiplying circuit p given also inFIG. 2, thereby to supply a signal corresponding to the right side ofthe formula 18, the comparison circuit of FIG. 6 may be made to supplyoutput l only when the formula 18 is satisfied.

FIG. 7 illustrates an example of the editing circuit explained alreadywith reference to FIG. 2. According to this particular example, twomultiplying/summing circuits illustrated in FIG. 1(8) are incorporated,thereby to ascertain whether or not at least two of inputs 3! g2, g havebeen supplied with signals l." The input signals so supplied will beeither l or Input signal supplied from the input g is constantly l. Theinputs g,, g, g,, are connected with resistances of R (in ohms), aterminal k, with a resistance of 2/3 R (in ohms), a terminal k, with aresistance of 2R(in ohms), and operational amplifiers G,and G withfeedback resistances of R (in ohms), respectively. Hence, in accordancewith the well known operations of the multiplying/summing circuits,there are obtained at output s I and I 2 of the operational amplifiersG, and G The output 1 is positive when signals l are supplied to two ormore of the inputs g,, g g,,, and the output I 2 is negative only whensignals 0" are supplied to all of these inputs. The outputs 1,and 1 areconnected to the aforesaid Schmidt circuits S, and 5,, respectively. Itis easy to provide each of these Schmidt circuits with two differentoutput terminals, i.e., a terminal generating output l when the inputsupplied is positive and a terminal generating output 1 when negative.If the terminal of the Schmidt circuit S,and the terminal of the otherSchmidt circuit S are connected to an OR circuit as in FIG. 7, theoutput r thereof can be caused to produce output l only when signals lare supplied to two or more of the inputs g,, g, ----g,, or when signalI is supplied to none of these inputs, i.e. only in the event ofidentification rejected. Further, by inverting the signal of the outputr by means of an inverting circuit INV, an output terminal m will havesignal l when identification is not rejected, i.e., when an inputpattern fed into the system is definitely identified. By applying thissignal to AND gates A,, A A,,, and by accordingly controlling the inputsignals supplied from the inputs g,, g g outputs 0,, 0,, 0,, will alwaysproduce only one definite result of identification for each inputpattern.

In the arrangement described herein, N number of different slightdeformations to be included in respective reference patterns arecompensated for according to the formula 7 for each of the referencepatterns. This compensation has to be made differently for eachreference patterns because different reference pattern have each aparticular set of N number of different slight deformations to beincluded therein. As a result, in the pattern identification schemebased upon multiple similarities, 6 will assume a positive value onlywhen deformation in excess of the permitted range of compensation hasbeen allowed to be included in a reference pattern. Stated conversely,if such deformation is within a certain allowable range, it is possibleto keep a value of e sufficiently small whenever an input patternsupplied belongs to the category of a particular reference pattern. Anyprior art known to the present applicant is unable to cope withdeformations that vary according to different reference patterns,thereby suffering greatly deteriorated discriminating power with respectto more or less deformed input patterns.

Another pattern identification system in accordance with the presentinvention can be configured on the basis of the formula 19 if so-calledadder circuits are substituted for the sum/square root circuits C ofFIG. 2. It will be readily understood that an adder circuit is obtainedif the squaring circuit disposed in a feedback path of the sumfsquareroot circuit illustrated in detail in FIG. 4 is replaced with anelectrical resistance R. In the precedingly described embodiment of theinvention, given input patterns have been sampled in accordance with theprior sampling theorem, and the integrating computations needed toobtain the desired scalar products with connection to such sampled inputpatterns have been converted into equivalent multiplying and summingcomputations so as to be carried out in electrical circuit means. Theabove scalar products, however, are obtainable by optical filter meansas described already with reference to FIG. 1(a). Regarding theaforementioned squaring circuits, adder circuits, sum/square rootcircuits, comparison circuits and editing circuit, too, some arithmeticunits can be materialized by means other than electrical circuits.Further, the norm il f ll of input pattern f(x) in the formulas l8 andI9 may be dispensed with since it is compared commonly with the outputsof K number of the sum/square root circuits or adder circuits 2,, Z Z

(in FIG. 8). As mentioned already, the multiple similarity S* [ff l hassome value in the range satisfying the formula 14 and, especially when agiven input pattern is identical with one of the reference patterns,assumes the maximum value 1. Since f [l is common to any value of k inthe multiple similarity (defined earlier by the formula 13) it willfollow that, by detecting a value of k which maximizes the input patternsupplied is identifiable as belonging to the kzh reference pattern.

From these considerations, the second pattern identification system hasbeen materialized by modifying the configuration of FIG. 2 into the oneillustrated schematically in FIG. 8. In this second system,multiplying/summing circuits X X X ----x,,,,, and squaring circuits y yy y remain substantially the same as in FIG. 2, while adder circuits Z1,z are provided in place of the sum/square root circuits of FIG. 2. Theoutputs e e of these adder circuits are connected to a maximumdetermining circuit G, which is caused to produce an output signal atone of its output terminals 0,, 0,, which corresponds to that one of theoutputs e e,, which has the maximum value. This editing circuit detectsthe maximum value m of input signals representing the capital K numberof sums, then proceeds at output signal l at the every output terminalscorresponding to the input signals of which value is larger than m(1+e)A suitable editing circuit of this type is disclosed for example in FIG.4 of Japanese Pat. Publication No. 19044/65.)

In case N 1 number of different slightly deformed patterns g,,"(x) to beincluded in reference pattern fi) (x) are not necessarily linearlyindependent, the total number M of different standard functions (1) n(x) having normal orthogonality as defined by the formula 9 will be: MN.

Consider the other case wher M N. Since {V satisfying the relation 1(n=n I I- =1 V nVmn (12,11 -1,2, N)

is obtainble, it follows that, if

the For mula (10) can be rewritten as 'tions i/ can be selected anewinstead of the N number of standard functions M Furthermore, from theFormulas (20) and (21), the relation is obtainable. Combined with theFormula (12), this relation provides the result What deserves attentionat this moment, however, is

so that the new standard functions b do not 25 necessarily showorthogonal relationship.

It will now be seen that by selecting the standard functions {M3 whichsatisfy the Formula (22), the expansion coefficient {12 thereof willsatisfy the Formula (24). In this instance, however, M may notnecessarily be equal to N, nor the standard functions always be inorthogonal relationship.

Although the present invention has been shown and described in theforegoing with connection to certain specific embodiments thereof, it isassumed that the invention is not to be restricted thereby but includesmodifications, substitutions and changes in accordance with itsfundamental concepts outlined earlier in this specification or withinits scope as defined by the appended claims.

What is claimed is:

1. A pattern identification system wherein N number of differentstandard patterns, N is not smaller than three, are prepared for each ofK number of different reference patterns with one of which a given inputpattern is to be identified, comprising means for obtaining the innerproducts of the input pattern and each of said N number of standardpatterns of each of said K number of reference patterns, means forobtaining the squares of each of the above obtained N X K number ofinner products, means for obtaining a sum of all N number of the aboveobtained squares for each of said K number of reference patterns, andmeans for identifying said input pattern with one of said K number ofreference patterns by selecting one of the above obtained K number ofsums which has a maximum value.

2. A pattern identification system as claimed in claim 1, in which saididentification rejecting means comprises a first circuit which producesoutput 1 when not less than two of its input signals respectivelyrepresenting said sums have equally a maximum value, a second circuitwhich produces output 1 when none of said input signals has a maximumvalue, and an OR circuit through which the outputs of said first andsaid 5 second circuits are transmitted, said first circuit comprising aplurality of resistances respectively connected to a plurality of inputterminals, another resistance connected to another input terminal towhich is always applied a constant signal, an operational amplifier towhich is commonly connected the other ends of all the said resistances,a feedback resistance connected between the output and input of saidoperational amplifier, and a Schmidt circuit producing output 1 when aninput signal supplied by said operational amplifier is positive, saidplurality of resistances having the same ohmic value, said otherresistance having an ohmic value different from the ohmic value of saidplurality of resistances, said feedback resistance having the same ohmicvalue as said plurality of resistances.

3. A pattern identification system as claimed in claim 2, in which theohmic values of each of said plurality of resistances, said otherresistance and said feedback resistance are approximately in the 122/311ratio.

4. A pattern identification system as claimed in claim 1, in which saidsecond circuit comprises a plurality of resistances respectivelyconnected to a plurality of input terminals, said plurality ofresistances having the same ohmic value, another resistance connected toanother input terminal to which is always applied a constant signal,said other resistance having an ohmic value different from the ohmicvalue of said plurality of resistances, an operational amplifier towhich is commonly connected the other ends of all the said resistances,a feedback resistance connected between the output and input of saidoperational amplifier, said feedback resistance having the same ohmicvalue as said plurality of resistances, and a Schmidt circuit producingoutput l when an input signal supplied by said operational amplifier isnegative.

5. A pattern identification system as claimed in claim 4, in which theohmic values of each of said plurality of resistances, said otherresistance and said feedback resistance are approximately in the 112:1ratio.

pattern and each of said N number of standard patterns of each of said Knumber of reference patterns, means for obtaining the square of each ofthe above obtained N X K number of inner products, means for obtainingthe square roots of the sums of all N number of the above obtainedsquares for said K number of reference patterns, means for obtaining thenorm of the input pattern, means for multiplying said norm of the inputpattern by a constant coefficient, and means for comparing between theabove obtained product of said norm of the input pattern and theconstant coefficient and the above obtained square roots correspondingto said K number of reference patterns, said means for obtaining thesquare roots of the sums of all N number of the precedingly obtainedsquares for said K number of reference patterns being formed by aplurality of electrical circuits each comprising an amplifier having ahigh amplification factor, a plurality of resistances havingsubstantially the same ohmic value and through which electrical signalsrepresenting the values of said squares are directed to the input ofsaid amplifier, and a squaring circuit connected between the output andinput of said amplifier.

1. A pattern identification system wherein N number of differentstandard patterns, N is not smaller than three, are prepared for each ofK number of differEnt reference patterns with one of which a given inputpattern is to be identified, comprising means for obtaining the innerproducts of the input pattern and each of said N number of standardpatterns of each of said K number of reference patterns, means forobtaining the squares of each of the above obtained N X K number ofinner products, means for obtaining a sum of all N number of the aboveobtained squares for each of said K number of reference patterns, andmeans for identifying said input pattern with one of said K number ofreference patterns by selecting one of the above obtained K number ofsums which has a maximum value.
 2. A pattern identification system asclaimed in claim 1, in which said identification rejecting meanscomprises a first circuit which produces output ''''1'''' when not lessthan two of its input signals respectively representing said sums haveequally a maximum value, a second circuit which produces output''''1'''' when none of said input signals has a maximum value, and an ORcircuit through which the outputs of said first and said second circuitsare transmitted, said first circuit comprising a plurality ofresistances respectively connected to a plurality of input terminals,another resistance connected to another input terminal to which isalways applied a constant signal, an operational amplifier to which iscommonly connected the other ends of all the said resistances, afeedback resistance connected between the output and input of saidoperational amplifier, and a Schmidt circuit producing output ''''1''''when an input signal supplied by said operational amplifier is positive,said plurality of resistances having the same ohmic value, said otherresistance having an ohmic value different from the ohmic value of saidplurality of resistances, said feedback resistance having the same ohmicvalue as said plurality of resistances.
 3. A pattern identificationsystem as claimed in claim 2, in which the ohmic values of each of saidplurality of resistances, said other resistance and said feedbackresistance are approximately in the 1:2/3:1 ratio.
 4. A patternidentification system as claimed in claim 1, in which said secondcircuit comprises a plurality of resistances respectively connected to aplurality of input terminals, said plurality of resistances having thesame ohmic value, another resistance connected to another input terminalto which is always applied a constant signal, said other resistancehaving an ohmic value different from the ohmic value of said pluralityof resistances, an operational amplifier to which is commonly connectedthe other ends of all the said resistances, a feedback resistanceconnected between the output and input of said operational amplifier,said feedback resistance having the same ohmic value as said pluralityof resistances, and a Schmidt circuit producing output ''''1'''' when aninput signal supplied by said operational amplifier is negative.
 5. Apattern identification system as claimed in claim 4, in which the ohmicvalues of each of said plurality of resistances, said other resistanceand said feedback resistance are approximately in the 1:2:1 ratio.
 6. Apattern identification system wherein N number of different standardpatterns are prepared for each of K number of different referencepatterns with one of which a given input pattern is to be identified,comprising means for obtaining the inner product of the input patternand each of said N number of standard patterns of each of said K numberof reference patterns, means for obtaining the square of each of theabove obtained N X K number of inner products, means for obtaining thesquare roots of the sums of all N number of the above obtained squaresfor said K number of reference patterns, means for obtaining the norm ofthe input pattern, means for multiplying said norm of the inpuT patternby a constant coefficient, and means for comparing between the aboveobtained product of said norm of the input pattern and the constantcoefficient and the above obtained square roots corresponding to said Knumber of reference patterns, said means for obtaining the square rootsof the sums of all N number of the precedingly obtained squares for saidK number of reference patterns being formed by a plurality of electricalcircuits each comprising an amplifier having a high amplificationfactor, a plurality of resistances having substantially the same ohmicvalue and through which electrical signals representing the values ofsaid squares are directed to the input of said amplifier, and a squaringcircuit connected between the output and input of said amplifier.